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#1 2006-03-30 09:07:36
- MathsIsFun
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Algebra Formulas
Algebra Formulas
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
#3 2006-04-02 23:13:38
- ganesh
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Re: Algebra Formulas
A quadratic equation consists of a single variable of degree 2 and is of the form
The roots of the equation are given by
Two roots or solutions are obtained, but sometimes they may be equal. If the discriminant b²-4ac>0, the roots are real and distinct. If b²-4ac=0, the roots are real and equal. If b²-4ac<0, the roots are distinct and imaginary.
The sum of the roots = -b/a
Product of the roots = c/a
Given the roots of the quadratic equation, the quadratic can be formed using the formula
x²-(sum of the roots)x + (product of the roots)=0.
Character is who you are when no one is looking.
#4 2006-04-05 01:52:24
- ganesh
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Re: Algebra Formulas
I. Arithmetic Progressions.
An Arithmetic Progression (AP) is a series in which the succesive terms have a common difference. The terms of an AP either increase or decrease progressively. For example,
1, 3, 5,7, 9, 11,....
10, 9, 8, 7,6, 5, .....
14.5, 21, 27.5, 34, 40.5 .....
11/3, 13/3, 15/3, 17/3, 19/3......
-5, -8,-11, -14, -17, -20 ......
Let the first term of the AP be a and the common difference, that is
the difference between any two succesive terms be d.
The nth term, tn is given by
The sum of n terms of an AP, Sn is given by the formula
or
where l is the last term (nth term in this case) of the AP.
Character is who you are when no one is looking.
#5 2006-04-05 01:58:16
- ganesh
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Re: Algebra Formulas
II. Geometric Progression
a, b, c, d, ... are said to be in Geometric Progression (GP) if
b/a = c/b = d/c etc.
A Geometric Progression is of the form
where a is the first term and r is the common ratio.
The nth term of a Geometric Progression is given by
The sum of the first n terms of a Geometric Progression is given by
(i) When r<1
(ii) When r>1
Sum of the infinite series of a Geometric Progression when |r|<1
Geometric Mean (GM) of two numbers a and b is given by
Character is who you are when no one is looking.
#6 2006-04-07 00:09:05
- ganesh
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Re: Algebra Formulas
Harmonic Progression:-
A Harmonic Progression (HP) is is a series of terms where the reciprocals of the terms are in Arithmetic Progression (AP).
The general form of an HP is
1/a, 1/(a+d), 1/(a+2d), 1/(a+3d), .....
The nth term of a Harmonic Progression is given by
tn=1/(nth term of the corresponding AP)
In the following Harmonic Progression
The Harmonic Mean (HM) of two numbers a and b is
The Harmonic Mean of n non-zero numbers
is
Relation between Arithmetic Mean (AM), Geometric Mean (GM) and Harmonic Mean (HM)
that is, AM, GM, HM are in Geometric Progression.
For two positive numbers,
AM ≥ GM ≥ HM equality holding for equal numbers.
For n non-zero positive numbers, AM ≥ GM ≥ HM
Character is who you are when no one is looking.
#7 2006-04-07 00:28:14
- ganesh
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Re: Algebra Formulas
SUMMATION
Character is who you are when no one is looking.
#8 2006-04-19 01:45:51
- ganesh
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Re: Algebra Formulas
Laws of Exponents
In all the above cases,
where a is a non-zero real number.
and n is a non-negative number.
If a is a postive real number and m,n are integers with n positive,
If and b are positive real numbers and n a natural number, then
If , then a=b.
If then m=n.
Character is who you are when no one is looking.
#9 2006-05-04 00:22:33
- ganesh
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Re: Algebra Formulas
Binomial theorem
If n is a positive integer,
where
Summation of Binomial coefficients
If n is a rational index and -1<x<1, then
Some expansions:-
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#10 2006-05-11 02:05:40
- ganesh
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Re: Algebra Formulas
Expansions of Logarithmic expressions
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#11 2006-05-12 01:48:23
- ganesh
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Re: Algebra Formulas
AP, GP, HP :- Some important results
If A is the Arithmetic Mean (AM) of two numbers a and b, and G is their Geometric Mean (GM), then the two numbers are given by
For example, let the two numbers be 4 and 16. The AM of the two numbers is 10 and their GM is 8.
Therefore, A=10, G=8
gives two values, viz. 16 and 4.
If
are in Geometric Progression, then
are in Arithmetic Progression.
Similarly, if
are in Arithmetic Progression, then
are in Geometric Progression.
Character is who you are when no one is looking.
#12 2006-05-14 22:52:28
- ganesh
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Re: Algebra Formulas
Arithmetico-Geometric Series
A series having terms
a, (a+d)r, (a+2d)r², .... etc. is an Arithmetico-Geometric series where a is the first term, d is the commom difference of the Arithmetic part of the series and r is the common ratio of the Geometric part of the series.
An example of Arithmetico-Geometric series is
10, 9/2, 2, 7/8, 3/8, 5/32.... wherea=10, d=-1, and r=1/2.
The nth term
In the above example, the third term is[a+2d]r², i.e.2.
The sum of the series to n terms is
In the series given above, the sum of the first four terms would be
20+[(-1/2)(7/8)][1/4]-7(1/16)/(1/2)=20-7/4-7/8=20-21/8=139/8.
It can be seen, 10+9/2+2+7/8=(80+36+16+7)/8=139/8.
The sum to infinity,
Character is who you are when no one is looking.
#14 2007-03-01 15:13:49
- MissK
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Re: Algebra Formulas
This is all very handy to a 4th grade teacher who took calculus only 25 short years ago! My current problem is to find out a formula for what another web site calls a "triangular number" pattern. 1, 3, 6, 10, 15 . . .
More to the point, how do I find all possible UNIQUE triple-dip combinations of ice cream cones. I know the formula for double-dips, but darned if I can't figure this one out.
Any help?? I am humbled by all of your brilliances.
Thank you -- K
Strength and Honor
#15 2007-03-01 15:25:48
- ganesh
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Re: Algebra Formulas
Hi MissK,
Welcome to the forum and thanks for posting what you think of the forum!
The series 1, 3, 6, 10, 15 has the first term (lets call it 'a' for convenience) as 1 and thereafter, the difference between the nth term and (n-1)th term is n. That is, the difference between the 3rd and 2nd term is 3, the difference between the 4th and the third terms is 4 and so on. Thus, the 2nd term is 2+a, the third term is 3+(2+a), the fourth term is 4+[3+(2+a)]. It can be seen that the nth term is
They form a series of numbers which are the sum of the first n natural numbers.
Character is who you are when no one is looking.
#16 2007-03-01 23:00:16
- MathsIsFun
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Re: Algebra Formulas
Triangular Numbers: Definition of Triangular Number
Combinations: Combinations and Permutations
Hope they help!
(But we may need to delete this conversation as it is in the formulas 
)
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
#17 2007-03-02 14:25:08
- MissK
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Re: Algebra Formulas
MathsIsFun wrote:
Triangular Numbers: Definition of Triangular Number
Combinations: Combinations and Permutations
Hope they help!
(But we may need to delete this conversation as it is in the formulas
Oh -- Oops! Sorry. That means I can only write brilliant formulas. OK
Thanks for the tolerance. Delete. 
Strength and Honor
#18 2007-03-08 19:20:03
- lightning
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Re: Algebra Formulas
'im learning a lot here
Zappzter - New IM app! Unsure of which room to join? "ZNU" is made to help new users. c:
#19 2007-05-10 13:01:55
- R3hall
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Re: Algebra Formulas
An example of figurometry formulas:
N2 = square number
√ = square root
Tn = triangle number
(-1+√(8n+1))/2= triangle root
#20 2008-04-19 10:53:12
- simron
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Re: Algebra Formulas
(a+b)^c = sum starting at k=1 to infinity((v choose k) x^k a^(v-k))
I couldn't get that to work in LaTeX.
Linux FTW
#21 2009-01-03 02:06:20
- ganesh
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Re: Algebra Formulas
Componendo-Dividendo
If
which is called the componendo.
If
, then,
which is called dividendo.
If
, then,
which is called the componendo & dividendo.
Character is who you are when no one is looking.
#22 2009-01-11 00:30:24
- ganesh
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Re: Algebra Formulas
1.
2. If a+b+c = 0,
3. (i)
is divisible by (x-a) for all values of n.
3. (ii)
is divisible by (x+a) for all even values of n.
3.(iii)
is divisible by (x+a) for all odd values of n.
Character is who you are when no one is looking.
#24 2009-01-11 01:51:39
- JaneFairfax
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Re: Algebra Formulas
This is also useful.
And this.
(slightly different from Ganesh’s formula)
#25 2009-11-25 05:18:43
- Denominator
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Re: Algebra Formulas
I learned limits today!!!!
I love Algebra and Calculus!!
I hate estimating and probability = [